Simplify; express your answer in exponential form. Assume $y\neq 0, n\neq 0$. $\dfrac{{(y^{-1})^{-1}}}{{(y^{-2}n^{-5})^{4}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${y^{-1}}$ to the exponent ${-1}$ . Now ${-1 \times -1 = 1}$ , so ${(y^{-1})^{-1} = y}$ In the denominator, we can use the distributive property of exponents. ${(y^{-2}n^{-5})^{4} = (y^{-2})^{4}(n^{-5})^{4}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(y^{-1})^{-1}}}{{(y^{-2}n^{-5})^{4}}} = \dfrac{{y}}{{y^{-8}n^{-20}}}$ Break up the equation by variable and simplify. $\dfrac{{y}}{{y^{-8}n^{-20}}} = \dfrac{{y}}{{y^{-8}}} \cdot \dfrac{{1}}{{n^{-20}}} = y^{{1} - {(-8)}} \cdot n^{- {(-20)}} = y^{9}n^{20}$.